No they shouldn't because they aren't. Without some evidence of actual planning for or an actual attempt to injure or kill, any such prosecution would inevitably fail and therefore be pointless. They should be prosecuted as what they are, malicious communication. That of itself can carry a custodial sentence, which once a few people do end up doing time, will be plenty enough to put all but the most swivel-eyed off.

It's got nothing to do with the web per se (although anonymity is possibly a large factor). Hate-filled unbalanced misogynists exist. Some of them have access to the internet, the same way they have access to the postal service. This kind of thing happened though the postal service before the internet existed. It's just someone's twitter or Facebook address is easier to find than their physical address.

I found the whole #twittersilence rather laughable to be honest with you. How is giving them what they want for a day going to put them off? How is someone not 'speaking' on twitter for a day somehow a big sacrifice? You'd have to be a serious narcissist to believe simply avoiding a public medium for 24 hours would cause enough consternation and hubbub to make it a worthwhile protest.

I don't know about 'first world problem' but #twittersilence was definitely a 'first world protest'.